Question

Which of the following graphs shows the preimage P(x)=x^2 and the image I(x)=P(1/3x)?

Answer 1

Answer:

The picture with the widest graph in red

Step-by-step explanation:

The graph P(x) is the parent graph for all quadratic functions. It has a vertex of (0,0) and has the following points:

x      f(x)

-2      4

-1       1

0       0

1         1

2       4

The image of l(x) = P(1/3x) changes the points of the function to

x      f(x)

-2/3      4/9

-1/3        1/9

0       0

1/3        1/9

2/3       4/9

This makes the graph much wider. The graph with the widest red graph is the graph.

Answer 2

Answer:

(See explanation and attachment below)

Step-by-step explanation:

The image is equal to:

$I(x) = \left(\frac{1}{3}\cdot x \right)^{2}$

$I(x) = \frac{1}{9}\cdot x^{2}$

Which means that $I(x) = \frac{1}{9}\cdot P(x)$, that is, a scale factor is applied to preimage in order to diminish growth rate of parabola at same values of x.

Some values of P(x) and I(x) are presented below:

    x                    P(x)                I(x)

    0                     0                   0

     1                     1                   1/9

     2                    4                  4/9

     3                    9                    1

The following image corresponds to both functions.